曲阜师范大学学报（自然科学版）2024，Vol.50Issue(1)：61-66,6.DOI:10.3969/j.issn.1001-5337.2024.1.061
稳定连续半格的闭包空间表示
A representation of stably continuous semilattices by closure spaces
摘要
Abstract
The main purpose of this paper is to establish an appropriate representation for stably contin-uous semilattices by closure spaces.The notion of a multiplicative closure space is introduced.It is shown that the collection of all regular closed sets of multiplicative closure space under set inclusion forms a stab-ly continuous semilattice and every stably continuous semilattice can be obtained in this way up to isomor-phism.Moreover,the notion of an approximable mapping between multiplicative closure spaces is presen-ted to characterize the equivalence between the category of stably continuous semilattices with Scott con-tinuous functions and that of multiplicative closure spaces with approximable mappings.关键词
闭包空间/Domain理论/稳定连续半格/Scott连续映射/范畴等价Key words
closure spaces/Domain theory/stably continuous semilattices/Scott continuous functions/categorical equivalence分类
数理科学引用本文复制引用
王胜文,张冰,马俊叶,王龙春..稳定连续半格的闭包空间表示[J].曲阜师范大学学报（自然科学版）,2024,50(1):61-66,6.基金项目
曲阜师范大学校级教改项目(22jg30) （22jg30）
曲阜师范大学大学生创新训练项目(XJ20210065) （XJ20210065）
六盘水师范学院重点学科建设项目—数学重点培育学科(LPSSYZDPYXK201709) （LPSSYZDPYXK201709）
山西省基础研究计划项目(202103021223272) （202103021223272）
太原科技大学博士科研启动基金(20202049). （20202049）
